On the Coerciveness of Merit Functions for the Second-Order Cone Complementarity Problem

The Second-Order Cone Complementarity Problem (SOCCP) is a wide class of problems, which includes the Nonlinear Complementarity Problem (NCP) and the Second-Order Cone Programming Problem (SOCP). Recently, Fukushima, Luo and Tseng extended some merit functions and their smoothing functions for NCP to SOCCP. Moreover, they derived computable formulas for the Jacobians of the smoothing functions and gave the conditions for the Jacobians to be invertible. In this paper, we focus on a merit function for SOCCP, and show that the merit function is coercive under the condition that the function involved in SOCCP is strongly monotone. Furthermore, we propose a globally convergent algorithm, which is based on smoothing and regularization methods, for solving merely monotone SOCCP, and examine its effectiveness by means of numerical experiments.